Let x1, x2, x3 and x4 be 0-1 variables whose values indicate whether the projects are not done (0) or are done (1). Which of the following answers indicates that no more than three of the projects must be done?Group of answer choicesx1 + x2 + x3 + x4 ≤ 2x1 + x1 + x3 + x4 ≤ 3x1 + x2 + x3 + x4 ≤ 4x1 + x2 + x3 + x4 ≤ 3
Question
Let x1, x2, x3 and x4 be 0-1 variables whose values indicate whether the projects are not done (0) or are done (1). Which of the following answers indicates that no more than three of the projects must be done?Group of answer choicesx1 + x2 + x3 + x4 ≤ 2x1 + x1 + x3 + x4 ≤ 3x1 + x2 + x3 + x4 ≤ 4x1 + x2 + x3 + x4 ≤ 3
Solution
The correct answer is "x1 + x2 + x3 + x4 ≤ 3."
Explanation:
The variables x1, x2, x3, and x4 represent whether each of the four projects is done (1) or not done (0). If no more than three of the projects must be done, then the sum of these variables should be less than or equal to 3. This is represented by the inequality x1 + x2 + x3 + x4 ≤ 3.
The other options are incorrect. The inequality x1 + x2 + x3 + x4 ≤ 2 would mean that no more than two projects can be done. The inequality x1 + x1 + x3 + x4 ≤ 3 is not correctly formulated, and the inequality x1 + x2 + x3 + x4 ≤ 4 would mean that all four projects can be done.
Similar Questions
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